Limit cycles of a Z3Z3-equivariant near-Hamiltonian system

This paper presents a study on the number of limit cycles of a Z3Z3-equivariant near-Hamiltonian system of degree 5 which is a perturbation of a cubic Hamiltonian system. By using the Melnikov method, we obtain 15 limit cycles. With degrees 3 and 4, we respectively get 4 and 10 limit cycles.